document.write( "Question 416360: combine an alloy that costs $4.30 and ounce with an alloy that cost $1.80 an ounce. Hou many ounces of each were used to make a mixture of 200 ounces costing $2.50 per ounce? \n" ); document.write( "

Algebra.Com's Answer #291714 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = ounces of $4.30/oz alloy needed
\n" ); document.write( "Let $\"b\"$ = ounces of $1.80/ oz alloy needed
\n" ); document.write( "In words:
\n" ); document.write( "(cost of 1st alloy + cost of 2nd alloy) / (total ounces of both) = cost/ounce
\n" ); document.write( "(1) $\"+%284.3a+%2B+1.8b%29%2F200+=+2.5+\"$
\n" ); document.write( "(2) $\"a+%2B+b+=+200\"$
\n" ); document.write( "-----------------
\n" ); document.write( "(1) $\"+%284.3a+%2B+1.8b%29%2F200+=+2.5+\"$
\n" ); document.write( "(1) $\"+4.3a+%2B+1.8b+=+500+\"$
\n" ); document.write( "(1) $\"43a+%2B+18b+=+5000\"$
\n" ); document.write( "-----------------
\n" ); document.write( "Multiply both sides of (2) by $\"18\"$ and
\n" ); document.write( "subtract from (1)
\n" ); document.write( "(1) $\"43a+%2B+18b+=+5000\"$
\n" ); document.write( "(2) $\"-18a+-+18b+=+-3600\"$
\n" ); document.write( " $\"+25a+=+1400\"$
\n" ); document.write( " $\"+a+=+56\"$
\n" ); document.write( "and,
\n" ); document.write( " $\"b+=+200+-+56\"$
\n" ); document.write( " $\"b+=+144\"$
\n" ); document.write( "56 ounces of $4.30/oz alloy are needed
\n" ); document.write( "144 ounces of $1.80/ oz alloy are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+%284.3a+%2B+1.8b%29%2F200+=+2.5+\"$
\n" ); document.write( "(1) $\"+%284.3%2A56+%2B+1.8%2A144%29%2F200+=+2.5+\"$
\n" ); document.write( "(1) $\"+%284.3%2A56+%2B+1.8%2A144%29%2F200+=+2.5+\"$
\n" ); document.write( " $\"+240.8+%2B+259.2+=+500+\"$
\n" ); document.write( " $\"+500+=+500+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );